docs: def fnc(ra, *args):
      """
      Function used in the minimisation problem.
  
      :param ra:
          Semi-axis of the ellipses used in the Yu et al.
      :returns:
          The absolute difference between the epicentral distance and the
          adjusted distance
      """
      #
      # epicentral distance
      repi = args[0]
      #
      # azimuth
      theta = args[1]
      #
      # magnitude
      mag = args[2]
      #
      # coefficients
      coeff = args[3]
      #
      # compute the difference between epicentral distances
      rb = rbf(ra, coeff, mag)
      t1 = ra**2 * (np.sin(np.radians(theta)))**2
      t2 = rb**2 * (np.cos(np.radians(theta)))**2
      xx = ra * rb / (t1+t2)**0.5
      return xx-repi